Magnetic dilution effect and topological phase transitions in (Mn${}_{1-x}$Pb${}_x$)Bi${}_2$Te${}_4$

Abstract

As the first intrinsic antiferromagnetic (AFM) topological insulator (TI), MnBi${}_2$Te${}_4$ has provided a material platform to realize various emergent phenomena arising from the interplay of magnetism and band topology. Here by investigating (Mn${}_{1-x}$Pb${}_x$)Bi${}_2$Te${}_4$ $(0\le x\le 0.82)$ single crystals via the x-ray, electrical transport, magnetometry and neutron measurements, chemical analysis, external pressure, and first-principles calculations, we reveal the magnetic dilution effect on the magnetism and band topology in MnBi${}_2$Te${}_4$. With increasing $x$, both lattice parameters $a$ and $c$ expand linearly by around 2\%. All samples undergo the paramagnetic to A-type antiferromagnetic transition with the N$\acute{e}$el temperature decreasing lineally from 24 K at $x=0$ to 2 K at $x=0.82$. Our neutron data refinement of the $x=0.37$ sample indicates that the ordered moment is 4.3(1)$\hat{I}{¼}_B$/Mn at 4.85 K and the amount of the Mn${}_{\mathrm{Bi}}$ antisites is negligible within the error bars. Isothermal magnetization data reveal a slight decrease of the interlayer plane-plane antiferromagnetic exchange interaction and a monotonic decrease of the magnetic anisotropy, due to diluting magnetic ions and enlarging the unit cell. For $x=0.37$, the application of external pressures enhances the interlayer antiferromagnetic coupling, boosting the N$\acute{e}$el temperature at a rate of 1.4 K/GPa and the saturation field at a rate of 1.8 T/GPa. Furthermore, our first-principles calculations reveal that the band inversion in the two end materials, MnBi${}_2$Te${}_4$ and PbBi${}_2$Te${}_4$, occurs at the $\hat{I}“$ and $Z$ point, respectively, while two gapless points appear at $x=$ 0.44 and $x=$ 0.66, suggesting possible topological phase transitions with doping.

10 pages, 7 figures